7. For what value of p does 122p-1 = 5(3.7)p ?

 

A.

(ln 5 - ln 12)/(ln 3.7 - ln 12)

B.

(ln 5 + ln 12)/(2 ln 12 - ln 3.7)

C.

(ln 12)/(2 ln 12 5 ln 3.7)

D

(ln 12)/(ln 12 5 ln 3.7).

E.

(ln 12 - ln 5)/(2 ln 12 + ln 3.7)

 

 

Solution: The answer is B

 

Using the properties of logarithms solve for p as follows:
Given,

Take the natural logarithm of both sides of the above equation,

Since, ln (uv) = ln u + ln v and ln un = n ln u, the above equation can be rewritten as follows,

Solving for p yields,